Problem: Kevin is 5 times as old as William. Eight years ago, Kevin was 9 times as old as William. How old is Kevin now?
Answer: We can use the given information to write down two equations that describe the ages of Kevin and William. Let Kevin's current age be $k$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $k = 5w$ Eight years ago, Kevin was $k - 8$ years old, and William was $w - 8$ years old. The information in the second sentence can be expressed in the following equation: $k - 8 = 9(w - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to solve our first equation for $w$ and substitute it into our second equation. Solving our first equation for $w$ , we get: $w = k / 5$ . Substituting this into our second equation, we get: $k - 8 = 9($ $(k / 5)$ $- 8)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $k - 8 = \dfrac{9}{5} k - 72$ Solving for $k$ , we get: $\dfrac{4}{5} k = 64$ $k = \dfrac{5}{4} \cdot 64 = 80$.